Finite Group Databasebeta

← #28374817

Subgroups — #28374817

Order 13952.

454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295839C211yesmaximal, characteristic, complemented
2#20295832C212yesmaximal, complemented
3#20295827C211yesmaximal, characteristic, complemented
4#20295298C211yesmaximal, characteristic, complemented
5#20295293C211yesmaximal, characteristic, complemented
6#20295286C212yesmaximal, complemented
7#20295203C212yesmaximal, complemented
8#20295198C212yesmaximal, complemented
9#20295144C211yesmaximal, characteristic, complemented
10#20295144C211yesmaximal, characteristic, complemented
11#495×C109C211yesmaximal, characteristic, complemented
12#16812747C2212yescomplemented
13#16812744C2212yes—
14#16812731—22no—
15#16812730C2212yes—
16#16812730C2212yescomplemented
17#16812728—22no—
18#16812726—22no—
19#16812725C2212yes—
20#16812725C2212yescomplemented
21#16812723—22no—
22#16812722—21no—
23#16812721C2211yescharacteristic
24#16812721C2211yescharacteristic
25#16812720—22no—
26#16812718—21no—
27Q16×D109—21no—
28SD16×D109—22no—
29D8×D109—21no—
30#16812705C2211yescharacteristic
31#16812705C2212yescomplemented
32#16812705C2211yescharacteristic, complemented
33#16812635C2211yescharacteristic, complemented
34#16812635C2211yescharacteristic, complemented
35#16812627C2211yescharacteristic
36#16812627C2211yescharacteristic, complemented
37#16812627C2212yescomplemented
38#16812618C2212yescomplemented
39#16812616C2212yescomplemented
40C2×Q16×C109C2211yescharacteristic, complemented
41C2×SD16×C109C2212yescomplemented
42C2×D8×C109C2211yescharacteristic
43#124×C109C2212yescomplemented
44C4×C8×C109C2211yescharacteristic, complemented
45#13182030—22no—
46#13182030—22no—
47#13182029—42no—
48#13182029C2311yescharacteristic
49#13182029C2312yes—
50#13182029C2311yescharacteristic
51#13182028—22no—
52#13182028—22no—
53Q8×D109—22no—
54Q8×D109—22no—
55C2×C22⋊D109—42no—
56D4×D109—22no—
57D4×D109—22no—
58Dic436D411yescharacteristic
59Dic436D411yescharacteristic
60#13182019—22no—
61#13182019—22no—
62#13182018D411yescharacteristic
63#13182018D411yescharacteristic
64#13182018D412yes—
65#13182017—22no—
66#13182017—22no—
67#13182016—22no—
68#13182016—22no—
69D872D411yescharacteristic
70D872D411yescharacteristic
71#13182014—22no—
72#13182014—22no—
73#13182013C2311yescharacteristic
74#13182013C2312yes—
75#13182013C2311yescharacteristic
76#13182012—21no—
77#13182012—22no—
78#13182012—21no—
79C8×D109—21no—
80C8×D109—22no—
81C8×D109—21no—
82C2×Q8×C109C2312yes—
83C2×D4×C109C2312yes—
84Q16×C109—21no—
85Q16×C109—21no—
86SD16×C109—22no—
87SD16×C109—22no—
88D8×C109—21no—
89D8×C109—21no—
90C2×C8×C109C2311yescharacteristic
91C2×C8×C109C2311yescharacteristic
92C22⋊C4×C109—42no—
93C42×C109C2311yescharacteristic
94C23×C109—22no—
95C22×D109—42no—
96Q8×C109—22no—
97Q8×C109—22no—
98D4×C109—22no—
99D4×C109—22no—
100C2×C4×C109—21no—
101C2×C4×C109—22no—
102C2×C4×C109C2411yescharacteristic
103C22⋊D109—21no—
104C22⋊D109—22no—
105C22⋊D109—21no—
106C22⋊D109—42no—
107C22⋊D109—42no—
108C2×Dic109—42no—
109D436—42no—
110D436C2×D411yescharacteristic
111D436C2×D412yes—
112D436C2×D411yescharacteristic
113C4×D109—21no—
114C4×D109—22no—
115C4×D109—21no—
116C4×D109—42no—
117C4×D109—42no—
118Dic218—42no—
119Dic218C2×D411yescharacteristic
120Dic218C2×D412yes—
121Dic218C2×D411yescharacteristic
122C8×C109C2×D411yescharacteristic
123C8×C109C2×D411yescharacteristic
124C8×C109C2×D411yescharacteristic
125C8×C109C2×D411yescharacteristic
126#11724784—21no—
127#11724784—22no—
128#11724784—21no—
129C22×C109—42no—
130C22×C109—82no—
131C22×C109H(5,𝔽2)11yescharacteristic
132C2×D109—21no—
133C2×D109—22no—
134C2×D109—21no—
135C2×D109—162no—
136C4×C109—41no—
137C4×C109—42no—
138C4×C109C22×D411yescharacteristic
139C4×C109C22×D411yescharacteristic
140Dic109—21no—
141Dic109—22no—
142Dic109—21no—
143C2×C109—21no—
144C2×C109—82no—
145C2×C109D4211yescharacteristic
146D109—41no—
147D109—42no—
148D109—41no—
149#3290—1091nomaximal, Sylow
150C109#329011yescharacteristic, complemented, Sylow
151#578—1091no—
152#577—1092no—
153#576—1091no—
154#495D10911yescharacteristic, complemented
155#473—1091no—
156#472—1091no—
157#471—1092no—
158#455—1092no—
159#454—1092no—
160#443—1091no—
161#443—1091no—
1622−1+4—1092no—
163H(5,𝔽2)—1092no—
164#137—1092no—
165#137—1092no—
166#137—2182no—
167#137—2182no—
168AGL(1,ℤ/8)—1092no—
169AGL(1,ℤ/8)—1092no—
170AGL(1,ℤ/8)—2182no—
171AGL(1,ℤ/8)—2182no—
172#135—1091no—
173#135—1091no—
174#135—2181no—
175#135—2181no—
176#135—2182no—
177C2×Q16—2181no—
178C2×Q16C2×D10911yescharacteristic, complemented
179C2×SD16—2182no—
180C2×SD16C2×D10912yescomplemented
181C2×D8—2181no—
182C2×D8C2×D10911yescharacteristic
183#131—1091no—
184#131—1092no—
185#131—1091no—
186#124C2×D10912yescomplemented
187#108—1091no—
188#108—1091no—
189#104—1091no—
190#104—1091no—
191#104—1092no—
192#101—1092no—
193#100—1092no—
194C4×C8C2×D10911yescharacteristic, complemented
195#41—1091no—
196#41—1092no—
197#41—1091no—
198#41—4362no—
199#41—2182no—
200#41—2182no—
201#41—2182no—
202#41—2182no—
203C2×Q8—2182no—
204C2×Q8—2182no—
205C2×Q8C22×D10912yes—
206C2×D4—4362no—
207C2×D4—2182no—
208C2×D4—2182no—
209C2×D4C22×D10912yes—
210Q16—21no—
211Q16—21no—
212Q16—1091no—
213Q16—1091no—
214Q16—2182no—
215Q16—2182no—
216SD16—22no—
217SD16—22no—
218SD16—1091no—
219SD16—1091no—
220SD16—1092no—
221SD16—2182no—
222SD16—2182no—
223SD16—2182no—
224SD16—2182no—
225D8—21no—
226D8—21no—
227D8—1091no—
228D8—1091no—
229D8—2182no—
230D8—2182no—
231M16—1091no—
232M16—1092no—
233M16—1091no—
234M16—2181no—
235M16—2182no—
236M16—2181no—
237C2×C8—2181no—
238C2×C8—2182no—
239C2×C8—2181no—
240C2×C8C22×D10911yescharacteristic
241C2×C8C22×D10911yescharacteristic
242C22⋊C4—42no—
243C42C22×D10911yescharacteristic
244C23—22no—
245C23—4362no—
246Q8—22no—
247Q8—22no—
248Q8—1091no—
249Q8—1092no—
250Q8—1091no—
251Q8—4362no—
252D4—22no—
253D4—22no—
254D4—1091no—
255D4—1092no—
256D4—1091no—
257D4—4362no—
258D4—4362no—
259D4—4362no—
260D4—2181no—
261D4—2182no—
262D4—2181no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—4362no—
266C2×C4—4362no—
267C2×C4—4362no—
268C2×C4—2181no—
269C2×C4—2182no—
270C2×C4—2181no—
271C2×C4C23×D10911yescharacteristic
272C8—2181no—
273C8—2182no—
274C8—2181no—
275C8D4×D10911yescharacteristic
276C8D4×D10911yescharacteristic
277C8D4×D10911yescharacteristic
278C8D4×D10911yescharacteristic
279C22—42no—
280C22—82no—
281C22—17442no—
282C22—2181no—
283C22—2182no—
284C22—2181no—
285C22#1681274411yescharacteristic
286C4—41no—
287C4—42no—
288C4—2181no—
289C4—2182no—
290C4—2181no—
291C4C2×D4×D10911yescharacteristic
292C4C2×D4×D10911yescharacteristic
293C2—21no—
294C2—82no—
295C2—4361no—
296C2—4362no—
297C2—4361no—
298C2#2029566111yescharacteristic
subgroupG/H
centerC2#20295661
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#495×C109C2
socleC2×C109D42
hypercenter#495D109
hypocenterC109#3290
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #495

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20295839C2semidirect
2. #20295832C2semidirect
3. #20295827C2semidirect
4. #20295298C2semidirect
5. #20295293C2semidirect
6. #20295286C2semidirect
7. #20295203C2semidirect
8. #20295198C2semidirect
9. #20295144C2semidirect
10. #20295144C2semidirect
11. #495×C109C2semidirect
12. #16812747C22semidirect
16. #16812730C22semidirect
20. #16812725C22semidirect
31. #16812705C22semidirect
32. #16812705C22semidirect
33. #16812635C22semidirect
34. #16812635C22semidirect
36. #16812627C22semidirect
37. #16812627C22semidirect
38. #16812618C22semidirect
39. #16812616C22semidirect
40. C2×Q16×C109C22semidirect
41. C2×SD16×C109C22semidirect
43. #124×C109C22semidirect
44. C4×C8×C109C22semidirect
150. C109#3290semidirect
154. #495D109semidirect
178. C2×Q16C2×D109semidirect
180. C2×SD16C2×D109semidirect
186. #124C2×D109semidirect
194. C4×C8C2×D109semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202958392
#202958322
#202958272
#202952982
#202952932
#202952862
#202952032
#202951982
#202951442
#495×C1092
#3290109